scholarly journals Identification of average effects under magnitude and sign restrictions on confounding

10.3982/qe689 ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 1619-1657 ◽  
Author(s):  
Karim Chalak
Keyword(s):  
Sensitivity Analysis ◽  
Direct Effect ◽  
Instrumental Variables ◽  
Average Treatment Effect ◽  
Structural Systems ◽  
Omitted Variables ◽  
Average Effect ◽  
Omitted Variable Bias ◽  
Marginal Effects ◽  
Variable Bias

This paper studies measuring various average effects of X on Y in general structural systems with unobserved confounders U, a potential instrument Z, and a proxy W for U. We do not require X or Z to be exogenous given the covariates or W to be a perfect one‐to‐one mapping of U. We study the identification of coefficients in linear structures as well as covariate‐conditioned average nonparametric discrete and marginal effects (e.g., average treatment effect on the treated), and local and marginal treatment effects. First, we characterize the bias, due to the omitted variables U, of (nonparametric) regression and instrumental variables estimands, thereby generalizing the classic linear regression omitted variable bias formula. We then study the identification of the average effects of X on Y when U may statistically depend on X and Z. These average effects are point identified if the average direct effect of U on Y is zero, in which case exogeneity holds, or if W is a perfect proxy, in which case the ratio (contrast) of the average direct effect of U on Y to the average effect of U on W is also identified. More generally, restricting how the average direct effect of U on Y compares in magnitude and/or sign to the average effect of U on W can partially identify the average effects of X on Y. These restrictions on confounding are weaker than requiring benchmark assumptions, such as exogeneity or a perfect proxy, and enable a sensitivity analysis. After discussing estimation and inference, we apply this framework to study earnings equations.

scholarly journals Omitted Variable Bias in GLMs of Neural Spiking Activity

2018 ◽  
Vol 30 (12) ◽  
pp. 3227-3258 ◽  
Author(s):  
Ian H. Stevenson
Keyword(s):  
Neural Activity ◽  
Single Neuron ◽  
Linear Models ◽  
Theory And Practice ◽  
Parameter Estimates ◽  
Omitted Variables ◽  
History Effects ◽  
Omitted Variable Bias ◽  
Wide Range ◽  
Variable Bias

Generalized linear models (GLMs) have a wide range of applications in systems neuroscience describing the encoding of stimulus and behavioral variables, as well as the dynamics of single neurons. However, in any given experiment, many variables that have an impact on neural activity are not observed or not modeled. Here we demonstrate, in both theory and practice, how these omitted variables can result in biased parameter estimates for the effects that are included. In three case studies, we estimate tuning functions for common experiments in motor cortex, hippocampus, and visual cortex. We find that including traditionally omitted variables changes estimates of the original parameters and that modulation originally attributed to one variable is reduced after new variables are included. In GLMs describing single-neuron dynamics, we then demonstrate how postspike history effects can also be biased by omitted variables. Here we find that omitted variable bias can lead to mistaken conclusions about the stability of single-neuron firing. Omitted variable bias can appear in any model with confounders—where omitted variables modulate neural activity and the effects of the omitted variables covary with the included effects. Understanding how and to what extent omitted variable bias affects parameter estimates is likely to be important for interpreting the parameters and predictions of many neural encoding models.

Model misspecification and bias in the least-squares algorithm: Implications for linearized isotropic AVO

2021 ◽  
Vol 40 (9) ◽  
pp. 646-654
Author(s):  
Henning Hoeber
Keyword(s):  
Least Squares ◽  
Model Misspecification ◽  
Forward Model ◽  
Model Parameters ◽  
Omitted Variables ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Omitted Variable Bias ◽  
Least Squares Fit ◽  
Variable Bias

When inversions use incorrectly specified models, the estimated least-squares model parameters are biased. Their expected values are not the true underlying quantitative parameters being estimated. This means the least-squares model parameters cannot be compared to the equivalent values from forward modeling. In addition, the bias propagates into other quantities, such as elastic reflectivities in amplitude variation with offset (AVO) analysis. I give an outline of the framework to analyze bias, provided by the theory of omitted variable bias (OVB). I use OVB to calculate exactly the bias due to model misspecification in linearized isotropic two-term AVO. The resulting equations can be used to forward model unbiased AVO quantities, using the least-squares fit results, the weights given by OVB analysis, and the omitted variables. I show how uncertainty due to bias propagates into derived quantities, such as the χ-angle and elastic reflectivity expressions. The result can be used to build tables of unique relative rock property relationships for any AVO model, which replace the unbiased, forward-model results.

scholarly journals The Impossible Mediation Test: A Method for Dealing with Plausibly Confounded Mediation

2017 ◽  
Author(s):  
David Scott Yeager ◽  
Jon Krosnick
Keyword(s):  
Sensitivity Analysis ◽  
Correlational Analysis ◽  
Causal Process ◽  
Psychology Research ◽  
Strong Basis ◽  
Spurious Association ◽  
Omitted Variable Bias ◽  
Variable Bias ◽  
As If

In much psychology research, mediators are measured, not manipulated. Therefore, the paths from mediators to outcomes—the so-called b paths—can be confounded by omitted variable bias, as in any other correlational analysis. The present research builds on the logic of falsification tests in econometrics and sensitivity analysis in statistics to propose the impossible mediation test, which can quantify the amount of confounded mediation. Researchers can add to an experiment a condition in which the dependent variable is measured first, then the manipulation is implemented, and finally, the posited mediator is measured. This allows for assessment of the spurious association between the dependent variable and the mediator, and statistics can be estimated as if the dependent variable was measured after the manipulation was implemented, to assess whether the spurious association is sufficiently strong to yield the false appearance of mediation. This estimate of “impossible” mediation can be compared to the results obtained from data where the dependent variable is actually measured in the conventional order after the mediator, to determine whether evidence of mediation is stronger in the latter case than the former. Evidence of mediation that survives the impossible mediation test constitutes a strong basis for a claim about mediation of a causal process. The paper illustrates this procedure with an empirical example.

Omitted Variables, Intent, and Counterfactuals: A Response to Michael H. Nelson

2007 ◽  
Vol 7 (1) ◽  
pp. 149-158 ◽  
Author(s):  
Allen Hicken
Keyword(s):  
Critical Mass ◽  
Omitted Variables ◽  
Asian Studies ◽  
Political Actors ◽  
Omitted Variable Bias ◽  
Variable Bias ◽  
East Asian Studies ◽  
Political Groups ◽  
Work Knowledge ◽  
Thoughtful Critique

I have written elsewhere: “Where there exists a critical mass of scholars working on similar sets of questions—critiquing and building on one another's work—knowledge accumulation is more likely to occur.”1 It is with this statement in mind that I proceed with my response to Michael Nelson's thoughtful critique on my previous article (see Allen Hicken, “Party Fabrication: Constitutional Reform and the Rise of Thai Rack Thai,” Journal of East Asian Studies 6, no. 3 [2006]: 381–407). Rather than a point-by-point rebuttal, I will focus on three of the most interesting and challenging of Nelson's theoretical critiques. The first substantive issue concerns the charge of omitted variable bias—specifically, in reference to the omission of local political groups from a macro-institutional account. The second and third criticisms are more methodological. First, can we or should we ascribe motives to political actors? Second, how can we use counterfactuals to solve problems of observational equivalence?

scholarly journals Spillover Effects in the Presence of Unobserved Networks

2020 ◽  
pp. 1-30
Author(s):  
Naoki Egami
Keyword(s):  
Sensitivity Analysis ◽  
Spillover Effect ◽  
Spillover Effects ◽  
Unbiased Estimation ◽  
Potential Influence ◽  
Face To Face ◽  
Multiple Networks ◽  
Omitted Variable Bias ◽  
Experimental Subjects ◽  
Variable Bias

Abstract When experimental subjects can interact with each other, the outcome of one individual may be affected by the treatment status of others. In many social science experiments, such spillover effects may occur through multiple networks, for example, through both online and offline face-to-face networks in a Twitter experiment. Thus, to understand how people use different networks, it is essential to estimate the spillover effect in each specific network separately. However, the unbiased estimation of these network-specific spillover effects requires an often-violated assumption that researchers observe all relevant networks. We show that, unlike conventional omitted variable bias, bias due to unobserved networks remains even when treatment assignment is randomized and when unobserved networks and a network of interest are independently generated. We then develop parametric and nonparametric sensitivity analysis methods, with which researchers can assess the potential influence of unobserved networks on causal findings. We illustrate the proposed methods with a simulation study based on a real-world Twitter network and an empirical application based on a network field experiment in China.

An Empirical Analysis of Model Misspecification in Studies of Valuation of Financial Statement Disclosures

1995 ◽  
Vol 10 (4) ◽  
pp. 719-749 ◽  
Author(s):  
Anne Beatty ◽  
Sandra Chamberlain ◽  
Joseph Magliolo
Keyword(s):  
Measurement Error ◽  
Model Misspecification ◽  
Financial Statement ◽  
Omitted Variables ◽  
Loan Loss ◽  
Share Prices ◽  
Valuation Model ◽  
Omitted Variable Bias ◽  
Weak Evidence ◽  
Variable Bias

A number of studies have examined the correlation between financial statement disclosures and share prices to assess the informativeness of these disclosures. There are several potential econometric problems with analyses of this type, and the interpretations of the results depend critically on the type of econometric problem. For example, the results of these studies should not be used to answer accounting policy questions unless the effect of an omitted variable bias is likely to be minimal. Given potential interpretation problems, we argue that analysis of model misspecification should be performed to isolate the form of misspecification. The contribution of this paper is to suggest a series of tests to perform this task. We use these tests to assess the importance of misspecification in adaptations of Barth's (1994) investment securities valuation model and Beaver et al.'s (1989) model of loan loss valuation. We find compelling evidence of the importance of misspecification apart from measurement error (e.g., omitted variables) in the model of investment securities valuation, but find only weak evidence of any misspecification other than measurement error in the loan loss valuation model.

scholarly journals Child stature, maternal education, and early childhood development in Nigeria

PLoS ONE ◽  
2021 ◽  
Vol 16 (12) ◽  
pp. e0260937
Author(s):  
Emmanuel Skoufias ◽  
Katja Vinha
Keyword(s):  
Early Childhood ◽  
Direct Effect ◽  
Maternal Education ◽  
Ad Hoc ◽  
Early Childhood Development ◽  
Childhood Development ◽  
Omitted Variable Bias ◽  
Point Estimates ◽  
Mother’S Education ◽  
Variable Bias

Data from the 2016–17 Multiple Indicator Cluster Survey from Nigeria are used to study the relationship between child stature, mother’s years of education, and indicators of early childhood development (ECD). The relationships are contrasted between two empirical approaches: the conventional approach whereby control variables are selected in an ad-hoc manner, and the double machine-learning (DML) approach that employs data-driven methods to select controls from a much wider set of variables and thus reducing potential omitted variable bias. Overall, the analysis confirms that maternal education and the incidence of chronic malnutrition have a significant direct effect on measures of early childhood development. The point estimates based on the ad-hoc specification tend to be larger in absolute value than those based on the DML specification. Frequently, the point estimates based on the ad-hoc specification fall inside the confidence interval of the DML point estimates, suggesting that in these cases the omitted variable bias is not serious enough to prevent making causal inferences based on the ad-hoc specification. However, there are instances where the omitted variable bias is sufficiently large for the ad hoc specification to yield a statistically significant relationship when in fact the more robust DML specification suggests there is none. The DML approach also reveals a more complex picture that highlights the role of context. In rural areas, mother’s education affects early childhood development both directly and indirectly through its impact on the nutritional status of both older and younger children. In contrast, in urban areas, where the average level of maternal education is much higher, increases in a mother’s education have only a direct effect on child ECD measures but no indirect effect through child nutrition. Thus, DML provides a practical and feasible approach to reducing threats to internal validity for robust inferences and policy design based on observational data.

scholarly journals Omitted variable bias in GLMs of neural spiking activity

2018 ◽  
Author(s):  
Ian H. Stevenson
Keyword(s):  
Neural Activity ◽  
Single Neuron ◽  
Linear Models ◽  
Theory And Practice ◽  
Parameter Estimates ◽  
Omitted Variables ◽  
History Effects ◽  
Omitted Variable Bias ◽  
Wide Range ◽  
Variable Bias

AbstractGeneralized linear models (GLMs) have a wide range of applications in systems neuroscience describing the encoding of stimulus and behavioral variables as well as the dynamics of single neurons. However, in any given experiment, many variables that impact neural activity are not observed or not modeled. Here we demonstrate, in both theory and practice, how these omitted variables can result in biased parameter estimates for the effects that are included. In three case studies, we estimate tuning functions for common experiments in motor cortex, hippocampus, and visual cortex. We find that including traditionally omitted variables changes estimates of the original parameters and that modulation originally attributed to one variable is reduced after new variables are included. In GLMs describing single-neuron dynamics, we then demonstrate how post-spike history effects can also be biased by omitted variables. Here we find that omitted variable bias can lead to mistaken conclusions about the stability of single neuron firing. Omitted variable bias can appear in any model with confounders – where omitted variables modulate neural activity and the effects of the omitted variables covary with the included effects. Understanding how and to what extent omitted variable bias affects parameter estimates is likely to be important for interpreting the parameters and predictions of many neural encoding models.

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